Sign convention for mirrors
Distances to the right and up are positive. To the left and down, negative.
A street map
On a street map, a delivery rider may call 'east' positive and 'west' negative, so that a distance carries a sign that says which way it is. Scientists do the same for mirrors, with the pole of the mirror as the starting point.
An object stands to the left of a mirror, 30 cm from the pole. How should this distance be written?
What this lesson covers
The idea
With the pole as origin and the principal axis as x-axis, the object is placed to the left and distances are measured from the pole: positive to the right and above the axis, negative to the left and below it.
A street map
On a street map, a delivery rider may call 'east' positive and 'west' negative, so that a distance carries a sign that says which way it is. Scientists do the same for mirrors, with the pole of the mirror as the starting point.
An object stands to the left of a mirror, 30 cm from the pole. How should this distance be written?
- As −30 cm, because it is measured to the left
- As +30 cm, because a distance has no direction
- As 0 cm, because the pole is the origin
Positive or negative?
Put each quantity in the right box. The pole is the origin and the principal axis is the x axis.
Rules for signs
Right and up count as positive. Left and down count as negative. The object is always placed to the left, so the light travels from the left.
In the New Cartesian Sign Convention the pole P is the origin and the principal axis is the x axis. The object is placed to the left of the mirror. Distances are measured from the pole: positive to the right and above the axis, negative to the left and below it.
Notes
New Cartesian Sign Convention: the pole is the origin, the object is on the left, and distances are positive to the right and above the axis, negative to the left and below it.
Check yourself
Where is the object always placed in this convention?
Which point is taken as the origin?
An object is 30 cm to the left of the pole of a mirror. What is its object distance? Give the signed number in cm.
Answer: -30 cm
Distances measured to the left of the origin are negative: −30 cm.
A distance is measured perpendicular to the principal axis and below it. Its sign is
- To the right of the mirror. Light from the object must fall on the reflecting surface, which faces left. The object is placed on the left.
- At the pole of the mirror. The pole is the origin from which distances are measured. The object is placed to the left of it.
- To the left of the mirror, so light falls on the mirror from the left — correct. Yes!
- The pole P of the mirror — correct. Yes!
- The centre of curvature C. C is a point on the principal axis at a distance R from the mirror. The origin is the pole.
- The principal focus F. F is a point on the principal axis. Distances are measured from the pole, which is the origin.
- positive. Distances above the principal axis are positive. Below the axis they are negative.
- negative — correct. Yes!
- zero. The distance is not zero, it has a size and a sign. Below the axis the sign is negative.